Edge of Many-Body Quantum Chaos in Quantum Reservoir Computing

TL;DR

This paper identifies the quantum many-body analog of the classical edge of chaos in quantum reservoir computing, demonstrating that optimal performance occurs near two distinct chaos-related boundaries in the Sachdev-Ye-Kitaev model.

Contribution

It introduces the concept of the edge of many-body quantum chaos as a new design principle for quantum reservoir computing using the SYK model.

Findings

Performance peaks near the Thouless time boundary.

Enhanced information processing at the integrable-chaotic transition.

Establishes the edge of many-body quantum chaos as a design guideline.

Abstract

Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension -- quantum reservoir computing (QRC) -- these principles are applied to quantum systems, whose rich dynamics broadens the landscape of information processing. In classical RC, optimal performance is typically achieved at the ``edge of chaos," the boundary between order and chaos. Here, we identify its quantum many-body counterpart using the QRC implemented on the celebrated Sachdev-Ye-Kitaev model. Our analysis reveals substantial performance enhancements near two distinct characteristic ``edges": a temporal boundary defined by the Thouless time, beyond which system dynamics is described by random matrix theory, and a parametric boundary governing the transition from integrable to chaotic regimes. These findings establish the ``edge of many-body quantum chaos" as a design guideline for QRC.